Find magnitude of acceleration on a Ca ion, given electric field.

[monnapomona]

Homework Statement

The electric field strength across a typical cell membrane is about 10⁷ N/C. Given this information, find the magnitude of the acceleration of a single charged Ca⁺¹ ion as it penetrated through the cell wall. Ignore any resistive forces.
One atomic mass unit is 1.66 x 10^-27 kg.

Homework Equations

F = ma
F=q₀E

The Attempt at a Solution

I was thinking of multiplying the charge with how many protons a Ca ion has so:

F=q₀E
= (20$\bullet$1.6*10^-19C)(10⁷ N/C)
= 3.2*10^-11 N

Then I manipulated for acceleration in F=ma and got 1.93*10¹⁶ m/s?

Is this the correct method for finding the magnitude of acceleration?

 

[cepheid]

Ca1+ means that the charge on the ion is only unbalanced by ONE proton charge. I.e. the atom has lost one electron, leaving it with a net positive charge due to ONE extra proton whose charge is unbalanced.

 

[monnapomona]

Ca1+ means that the charge on the ion is only unbalanced by ONE proton charge. I.e. the atom has lost one electron, leaving it with a net positive charge due to ONE extra proton whose charge is unbalanced.

So would it be correct if I just use q=+1.6*10^-19 C in the formula to find force?

 

[cepheid]

So would it be correct if I just use q=+1.6*10^-19 C in the formula to find force?

Yes.

 

[monnapomona]

Yes.

Okay so I used q=+1.6*10^-19 C in the formula and got F = 1.6*10^-12 N. To find the magnitude of acceleration, I manipulated for a in F = ma and got 9.64 * 10¹⁴ m/s as the answer but I inputted it in my online homework assignment and apparently it's wrong.

Should I use a different formula to find acceleration?

Edit: I used 1.66*10^-27 kg as the mass.

 

[haruspex]

I used 1.66*10^-27 kg as the mass.

That's one atomic mass unit. How many of those per calcium atom?

 

[monnapomona]

That's one atomic mass unit. How many of those per calcium atom?

To get atomic mass, do I need to add protons and neutrons in Calcium together? So 40?

 

[cepheid]

To get atomic mass, do I need to add protons and neutrons in Calcium together? So 40?

Sounds about right to me.

 

[monnapomona]

Sounds about right to me.

Sweet, I got the answer right! (2.41*10¹³ m/s) Thanks for all your help everyone! :D